Chapter 2, Problem 13QAP

Write each of the following numbers instandardscientific notation.

a. $1/1033$

e. $1/3,093,000$

b. $1/{10}^5$

f. $1/{10}^{-4}$

c. $1/{10}^{-7}$

g. $1/{10}^9$

d. $1/0.0002$

h. $1/0.000015$

Interpretation Introduction

(a)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$9.6805\times {10}^{-4}$.

Explanation of Solution

The given measurement is $\frac{1}{1033}$. It is equal to 0.00096805, to convert this into scientific notation; the decimal will be shift four places to the right. Since, the decimal move right, the power of 10 will be negative. The scientific notation will be $9.6805\times {10}^{-4}$.

Interpretation Introduction

(b)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$1.0\times {10}^{-5}$.

Explanation of Solution

The given measurement is $\frac{1}{{10}^5}$. It is equal to ${10}^{-5}$, to convert this into scientific notation; the decimal number should be written ranges from 1 to 10 thus, the scientific notation will be $1.0\times {10}^{-5}$.

Interpretation Introduction

(c)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$1.0\times {10}^7$.

Explanation of Solution

The given measurement is $\frac{1}{{10}^{-7}}$. It is equal to ${10}^7$, to convert this into scientific notation; the decimal number should be written ranges from 1 to 10 thus, the scientific notation will be $1.0\times {10}^7$.

Interpretation Introduction

(d)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$5.0\times {10}^3$.

Explanation of Solution

The given measurement is $\frac{1}{0.0002}$. It is equal to $5000$, to convert this into scientific notation; the decimal number should be written ranges from 1 to 10 thus, decimal will be placed after first digit that is 5. Now, after placing the decimal there will be three digits thus, power of 10 will be 3 and the scientific notation will be $5.0\times {10}^3$.

Interpretation Introduction

(e)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$3.2\times {10}^{-7}$.

Explanation of Solution

The given measurement is $\frac{1}{3,093,000}$. It is equal to $0.00000032$, to convert this into scientific notation; the decimal number should be written ranges from 1 to 10 thus, decimal will move seven steps to the right and power of 10 will be -7. Thus, the scientific notation will be $3.2\times {10}^{-7}$.

Interpretation Introduction

(f)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$1.0\times {10}^4$.

Explanation of Solution

The given measurement is $\frac{1}{{10}^{-4}}$. It is equal to ${10}^4$, to convert this into scientific notation; the decimal number should be written ranges from 1 to 10 thus the scientific notation will be $1.0\times {10}^4$.

Interpretation Introduction

(g)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$1.0\times {10}^{-9}$.

Explanation of Solution

The given measurement is $\frac{1}{{10}^9}$. It is equal to ${10}^{-9}$, to convert this into scientific notation; the decimal number should be written ranges from 1 to 10 thus the scientific notation will be $1.0\times {10}^{-9}$.

Interpretation Introduction

(h)

Interpretation:

The given number should be converted into standard scientific notation.

Concept Introduction:

Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer to Problem 13QAP

$6.66666667\times {10}^4$.

Explanation of Solution

The given measurement is $\frac{1}{0.000015}$. It is equal to $66,666.6667$, to convert this into scientific notation; the decimal number should be written ranges from 1 to 10 thus decimal will be placed after first digit, the decimal will move four places to the left. Since, the decimal shifts to left, the power of 10 will be positive. The scientific notation will be $6.66666667\times {10}^4$.